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Efficient version of non-strict evaluation
In computer science, graph reduction implements an efficient version of non-strict evaluation, an evaluation strategy where the arguments to a function
Graph_reduction
Special-purpose computer
A graph reduction machine is a special-purpose computer built to perform combinator calculations by graph reduction. Examples include the SKIM ("S-K-I
Graph_reduction_machine
Directed graph with no directed cycles
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it
Directed_acyclic_graph
Copy of a directed graph with redundant edges removed
In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges
Transitive_reduction
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Mathematical-logic system based on functions
graphs extended with letrec, to detect possibly infinite unwinding trees; 2) the representational calculus with β-reduction of scoped lambda graphs constitute
Lambda_calculus
computer science, a linear graph grammar (also a connection graph reduction system or a port graph grammar) is a class of graph grammar on which nodes have
Linear_graph_grammar
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Topics referred to by the same term
in A? Bit Rate Reduction, an audio compression method Data reduction, simplifying data in order to facilitate analysis Graph reduction, an efficient version
Reduction
Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De
List_of_graph_theory_topics
Type of knowledge base
knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used
Knowledge_graph
Projection of data onto lower-dimensional manifolds
Nonlinear dimensionality reduction (NLDR), also known as manifold learning, is any of various related techniques that aim to project high-dimensional
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Class of artificial neural networks
Graph neural networks (GNNs) are artificial neural networks designed for tasks whose inputs are graphs. Because graphs usually do not have a canonical
Graph_neural_network
Method for solving one problem using another
reduction to every other nontrivial problem, see p. 48. Schaefer, Marcus (2010), "Complexity of some geometric and topological problems" (PDF), Graph
Polynomial-time_reduction
Constraint programming setting
algorithms, tree decomposition, C-tree decomposition, graph reduction, re-parametrization and reduction, computing fundamental circuits, body-and-cad structure
Geometric_constraint_solving
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges
Graph_partition
Relation specifying a rewrite for each object, compatible with a reduction relation
Sorbonne Paris Cité. p. 62. Partain, William D. (December 1989). Graph Reduction Without Pointers (PDF) (PhD). University of North Carolina at Chapel
Reduction_strategy
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Swedish computer scientist
lazy languages had been implemented via interpreted graph reduction. LML compiled to graph reduction machine (G-machine) code. Part of the development team
Lennart_Augustsson
Programming paradigm based on applying and composing functions
implementation strategy for lazy evaluation in functional languages is graph reduction. Lazy evaluation is used by default in several pure functional languages
Functional_programming
Heuristic test for graph isomorphism
In graph theory, the Weisfeiler Leman graph isomorphism test is a heuristic test for the existence of an isomorphism between two graphs G and H. It is
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Methodic assignment of colors to elements of a graph
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain
Graph_coloring
Logical formalism using combinators instead of variables
Combinatory categorial grammar Explicit substitution Fixed point combinator Graph reduction machine Lambda calculus and Cylindric algebra, other approaches to
Combinatory_logic
Directed graph representing dependencies
the dependency graph is a graph G = ( S , T ) {\displaystyle G=(S,T)} with T ⊆ R {\displaystyle T\subseteq R} the transitive reduction of R. For example
Dependency_graph
Simple Turing complete logic
(PostScript) (by Milner, Parrow, and Walker) shows a scheme for combinator graph reduction for the SKI calculus in pages 25–28. the Nock programming language
SKI_combinator_calculus
Python library for graphs and networks
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. NetworkX began development
NetworkX
British computer scientist (1946–2023)
first for functional programming based on lazy evaluation, combinator graph reduction, and polymorphic types: SASL (1972), Kent Recursive Calculator (KRC)
David Turner (computer scientist)
David_Turner_(computer_scientist)
Complexity class
problem Dominating set problem Graph coloring problem Sudoku To the right is a diagram of some of the problems and the reductions typically used to prove their
NP-completeness
Subunit of a computational problem
or its negation. A reduction from this problem to a hard problem on undirected graphs, such as the Hamiltonian cycle problem or graph coloring, would typically
Gadget_(computer_science)
Knaster–Tarski theorem Cartesian closed category Yoneda lemma Graph reduction Combinator graph reduction Strict programming language Lazy evaluation, eager evaluation
List of functional programming topics
List_of_functional_programming_topics
Software optimization technique
programming Futures and promises Generator (computer programming) Graph reduction Incremental computing – a related concept whereby computations are
Lazy_evaluation
Measure of the structural complexity of a software program
Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program
Cyclomatic_complexity
Process of reducing the number of random variables under consideration
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the
Dimensionality_reduction
A simple example of a gap-producing reduction is the nonmetric Traveling Salesman problem (i.e. where the graph's edge costs need not satisfy the conditions
Gap_reduction
Unsolved problem in computational complexity theory
of problems with a polynomial-time Turing reduction to the graph isomorphism problem. If in fact the graph isomorphism problem is solvable in polynomial
Graph_isomorphism_problem
Graphs that differ only by edge subdivision
In graph theory, two graphs G {\displaystyle G} and G ′ {\displaystyle G'} are homeomorphic if there is a graph isomorphism from some subdivision of G
Homeomorphism_(graph_theory)
American inventor and businessman
his early developments of graphical-numerical computing devices, data-reduction tools, and plotters. He was awarded America's National Medal of Technology
Joseph_Gerber
British academic and author
parallel graph reduction machine. M. Cripps, J. Darlington, A. J. Field, P. G. Harrison, M. J. Reeve. Selected Reprints on Dataflow and Reduction Architectures
John_Darlington
American computer scientist
Edinburgh. hdl:1842/3937. OCLC 781103005. Lester, David (1988). Combinator graph reduction: A congruence and its applications. bodleian.ox.ac.uk (DPhil thesis)
Philip_Wadler
Type of chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that
Bar_chart
Inherent difficulty of computational problems
is the following. The input is an arbitrary graph. The problem consists in deciding whether the given graph is connected or not. The formal language associated
Computational complexity theory
Computational_complexity_theory
Length of shortest path between two nodes of a graph
mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting
Distance_(graph_theory)
Node ordering for directed acyclic graphs
computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u
Topological_sorting
Mapping a graph onto itself without changing edge-vertex connectivity
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving
Graph_automorphism
Programming language evaluation rules
exist. .NET languages implement call by need using the type Lazy<T>. Graph reduction is an efficient implementation of lazy evaluation. Call by macro expansion
Evaluation_strategy
Subset of a graph's nodes such that all other nodes link to at least one
In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination
Dominating_set
On forbidden subgraphs in planar graphs
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states
Kuratowski's_theorem
Maximal subgraph whose vertices can reach each other
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph
Component_(graph_theory)
Mathematical transform
In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors
Graph_Fourier_transform
t in a directed graph, if t is reachable from s. Formally, the decision problem is given by PATH = {⟨D, s, t⟩ | D is a directed graph with a path from
St-connectivity
Function in algebraic graph theory
chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function
Chromatic_polynomial
Spectral graph theory concept
spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are
Ramanujan_graph
Mathematical proof about the permanent of matrices
equivalent matrix whose entries are all powers of 2. The reduction can be expressed in terms of graphs equivalent to the matrices. Let G {\displaystyle G}
♯P-completeness of 01-permanent
♯P-completeness_of_01-permanent
Binary operation in graph theory
In graph theory, the modular product of graphs G and H is a graph formed by combining G and H that has applications to subgraph isomorphism. It is one
Modular_product_of_graphs
Graph showing the free energy vs oxidation state of a chemical species
similarly found by this graph. The slope of the line between any two points on a Frost diagram gives the standard reduction potential, E°, for the corresponding
Frost_diagram
Visual depiction of a partially ordered set
finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set ( S , ≤ ) {\displaystyle (S,\leq
Hasse_diagram
Software performance visualization technique
Makes "AI Flame Graphs" Open-Source". Phoronix. Retrieved 1 April 2026. "Scaling vLLM for Embeddings: 16x Throughput and Cost Reduction". Snowflake. Retrieved
Flame_graph
Leader election algorithm
introduced by Nicola Santoro. It proceeds by consecutive elimination and a graph-reduction technique called pruning. The algorithm is divided in a pre-processing
Yo-yo_(algorithm)
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Sound insulation measure
The sound reduction index is used to measure the level of sound insulation provided by a structure such as a wall, window, door, or ventilator. It is
Sound_reduction_index
Clustering methods
(eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is provided
Spectral_clustering
Notion in computational complexity theory
directed graph. Seta Takahiro provided a reduction from 3SAT to this problem when restricted to planar directed max degree-3 graphs. The reduction provides
Parsimonious_reduction
Combinatorial optimization problem
A more efficient reduction is called the doubling technique. Here, a new graph G' is built from two copies of the original graph G: a forward copy Gf
Assignment_problem
Data structure representing a finite set of strings
form of a directed acyclic graph with a single source vertex (a vertex with no incoming edges), in which each edge of the graph is labeled by a letter or
Deterministic acyclic finite state automaton
Deterministic_acyclic_finite_state_automaton
Nonlinear dimensionality reduction method
Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods. Isomap is used for computing
Isomap
Subset of a graph's vertices, including at least one endpoint of every edge
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In
Vertex_cover
Software static analysis tool used for safety critical applications
constructs a directed graph and associated semantics for the program under analysis. The graph is reduced using a series of graph reduction techniques. The
MALPAS Software Static Analysis Toolset
MALPAS_Software_Static_Analysis_Toolset
On converting relations to functions of several real variables
by F ( x , y ) = 0 {\displaystyle F(x,y)=0} can also be specified as the graph of a function f {\displaystyle f} , so that for each point ( x , y ) {\displaystyle
Implicit_function_theorem
Boolean satisfiability problem restricted to a planar incidence graph
is NP-complete, and is commonly used in reductions. Every 3SAT problem can be converted to an incidence graph in the following manner: For every variable
Planar_SAT
Constructs with triply-connected vertices
connected 3-regular (cubic) simple graphs are listed for small vertex numbers. The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is
Table_of_simple_cubic_graphs
Whether one vertex can be reached from another in a graph
In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s {\displaystyle s} can reach a vertex
Reachability
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Generalization of graph theory
hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two
Hypergraph
Computational technique
diffusion maps to achieve dimensionality reduction then also creates a KNN graph. Waterfall performs dimensionality reduction via principal component analysis
Trajectory_inference
Geometric placement based on ideal distances
application in the field of graph drawing. That is, one can find a reasonably aesthetically appealing layout for a network or graph by minimizing a stress
Stress_majorization
Computational problem in graph theory
minimum-weight closure in a vertex-weighted directed graph. It may be solved in polynomial time using a reduction to the maximum flow problem. It may be used to
Closure_problem
Graph data structure
In computer science, an e-graph is a data structure that stores an equivalence relation over terms of some language. Let Σ {\displaystyle \Sigma } be
E-graph
Fewest cliques covering a graph's edges
In the mathematical field of graph theory, the intersection number of a graph G = ( V , E ) {\displaystyle G=(V,E)} is the smallest number of elements
Intersection number (graph theory)
Intersection_number_(graph_theory)
Open-source data analytics cluster computing framework
Malak, Michael (14 June 2016). "Finding Graph Isomorphisms In GraphX And GraphFrames: Graph Processing vs. Graph Database". slideshare.net. sparksummit
Apache_Spark
Complexity class
Max-Uniform-Graph-Partitioning/Swap has been proven to be PLS-complete via a tight PLS-reduction from Max-Cut/Flip to Max-Uniform-Graph-partitioning/Swap
PLS_(complexity)
Graph with a median for each three vertices
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle
Median_graph
Problem of finding the longest simple path for a given graph
unweighted longest path problem can be shown using a reduction from the Hamiltonian path problem: a graph G has a Hamiltonian path if and only if its longest
Longest_path_problem
Directed graph describing citations in documents
A citation graph (or citation network), in information science and bibliometrics, is a directed graph that describes the citations within a collection
Citation_graph
Undirected unit-distance graph requiring four colors
In graph theory, a branch of mathematics, the Moser spindle (also called the Mosers' spindle or Moser graph) is an undirected graph, named after mathematicians
Moser_spindle
Complexity class
Longest simple path Graph coloring; an application: register allocation in compilers Lists of problems Lists of unsolved problems Reduction (complexity) Unknowability
NP-hardness
Smallest transitive relation containing a given binary relation
exist. Both transitive closure and transitive reduction are also used in the closely related area of graph theory. A relation R on a set X is transitive
Transitive_closure
Set of computational problems stated by Richard Karp (1973)
is a polynomial time many-one reduction from the Boolean satisfiability problem to each of 21 combinatorial and graph theoretical computational problems
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Method for partitioning partial orders into levels
Represent the partial order by its transitive reduction or covering relation, a directed acyclic graph G that has an edge from x to y whenever x < y and
Coffman–Graham_algorithm
Deleting a graph edge and merging its nodes
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously
Edge_contraction
Graph path which is an induced subgraph
finding large independent sets in graphs, by the following reduction. From any graph G with n vertices, form another graph H with twice as many vertices as
Induced_path
Combinatorial reconfiguration problem
max-degree 3 graphs. The reduction follows from QSAT and is outlined below. The above problem is PSPACE-Complete even if the constraint graph is planar,
Nondeterministic constraint logic
Nondeterministic_constraint_logic
Problem in theoretical computer science
many-one reduction shows that subgraph isomorphism is also NP-complete. An alternative reduction from the Hamiltonian cycle problem translates a graph G which
Subgraph_isomorphism_problem
Complexity class
problem in #P has a polynomial-time Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of polynomial-time transformations
♯P-complete
Measure in risk analysis
safety integrity level (SIL) is defined as the relative level of risk-reduction provided by a safety instrumented function (SIF), i.e. the measurement
Safety_integrity_level
Graph which can be made planar by removing a single node
In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called
Apex_graph
In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space.
Graph_homology
Type of graph in mathematics
Conversely, in a diamond-free partial order, the transitive reduction identifies a directed acyclic graph in which the subgraph reachable from any vertex induces
Multitree
Structure-preserving correspondence between node-link graphs
In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure. More concretely, it is a
Graph_homomorphism
Graph without triples of adjacent vertices
area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently
Triangle-free_graph
Graph-theoretic description of polyhedra
planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are
Steinitz's_theorem
GRAPH REDUCTION
GRAPH REDUCTION
Girl/Female
Muslim
Grape vine
Girl/Female
Muslim
Grape like
Biblical
a grape; a knot
Female
Thai/Siamese
Thai name A-GUN means "grape."
Girl/Female
Indian
Grape like
Boy/Male
African, Arabic
Grape Vines
Boy/Male
Biblical
A grape, a knot.
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Girl/Female
Tamil
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Grape, Belonging to kashmir
Kaslunira | கஸà¯à®²à¯à®‚நீரா
Girl/Female
Indian
Grape vine
Boy/Male
Arabic, Modern
Grape
Boy/Male
Muslim
Grape
Girl/Female
Afghan, Arabic, Hebrew, Indian, Muslim, Parsi, Sanskrit
Grape Presser; World; Song; Universe
Boy/Male
Hindu, Indian
Efficient; Conqueror of Miseries; Bond in Affection; Capable; Mysterious; Different than Others; Smart; Most Mysterious Vastu Grah 'Rahu'; Son of Lord Buddha; Son of Goddess Durga; Truth Follower; Best of All
Girl/Female
Hindu
Grape, Belonging to kashmir
Boy/Male
Biblical
A grape, a knot.
Boy/Male
Afghan, Hebrew, Indian, Parsi, Sanskrit
Grape Presser; World; Song
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Boy/Male
Indian
Grape
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
GRAPH REDUCTION
GRAPH REDUCTION
Boy/Male
Christian, Indian
Warrior
Male
English
Anglicized form of Hebrew Yehuw, JEHU means "God is He." In the bible, this is the name of several characters, including a king of Israel and a son of Hanani.
Girl/Female
Gujarati, Hindu, Indian, Sanskrit
Sand
Girl/Female
Irish
Bitter.
Male
English
 Anglicized form of Hebrew Ammown, AMMON means "kindred, tribal." In the bible, this is the name of a son of Lot by his younger daughter. Compare with another form of Ammon.
Boy/Male
Muslim
Name of swahabi
Girl/Female
Australian, Slavic
Born at Christmas
Boy/Male
Muslim American Arabic
Excellent. Noble. Early Imam (Leader) of Islam.
Boy/Male
Hindu, Indian
Type of Liquid
Boy/Male
Indian, Traditional
Rich; Lightning
GRAPH REDUCTION
GRAPH REDUCTION
GRAPH REDUCTION
GRAPH REDUCTION
GRAPH REDUCTION
n.
A grape dried in the sun; a raisin.
n.
A seed of the grape.
n.
A mangy tumor on the leg of a horse.
n.
A well-known edible berry growing in pendent clusters or bunches on the grapevine. The berries are smooth-skinned, have a juicy pulp, and are cultivated in great quantities for table use and for making wine and raisins.
n.
A plant of the genus Muscari; grape hyacinth.
n.
A grape, or a bunch of grapes.
n.
The cultivation of the vine; grape growing.
n.
See Grasshopper, and Frog hopper, Grape hopper, Leaf hopper, Tree hopper, under Frog, Grape, Leaf, and Tree.
a.
Full of small kernels like a grape.
n.
A variety of shaddock, called also grape fruit.
a.
Resembling a grape.
n.
A sort of grape.
n.
The plant which bears this fruit; the grapevine.
a.
Composed of, or resembling, grapes.
n.
A white grape, esteemed for the table.
n.
A grape of many varieties and colors.
n.
The Hartford grape, a variety of grape first raised at Hartford, Connecticut, from the Northern fox grape. Its large dark-colored berries ripen earlier than those of most other kinds.
n.
Grapeshot.